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Introduction To Relations

Class 12 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIf (A) has (4) elements, what is the number of reflexive and antisymmetric relations on (A)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (A) has (4) elements, how many relations on (A) are both reflexive and symmetric?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf a relation on (A={1,2,3}) is reflexive, symmetric and antisymmetric all together, which relation can it be?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3),(3,4),(1,3),(2,4)}) on (A={1,2,3,4}), why is (R) not a partial order relation?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3),(3,4),(1,3),(2,4),(1,4)}) on (A={1,2,3,4}), what type of relation is (R)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1),(2,3)}) on (A={1,2,3}), which pair is missing for symmetry?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3),(3,1)}) on (A={1,2,3}), which property definitely fails?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R) is reflexive and transitive, what decides whether (R) is symmetric?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R) is a partial order relation on (A={1,2,3}) and ((1,2),(2,1)\in R), what conclusion follows?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R) on (A={1,2,3}) is reflexive and symmetric and ((1,2),(2,3)\in R), which pair is necessary to make (R) an equivalence relation?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf all equivalence classes of (R) on (A={1,2,3,4}) are singletons, what relation is (R)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf a relation (R) on (A={1,2,3,4}) puts all elements in one equivalence class, what relation is (R)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf a relation (R) on (A={1,2,3,4}) forms two classes ({1,3}) and ({2,4}), how many pairs will be in (R)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,2),(2,3),(3,1)}) on (A={1,2,3}), why is (R) not transitive?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,2),(2,3),(1,3)}) on (A={1,2,3}), is (R) transitive?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,2),(2,1),(2,3),(3,2),(1,3),(3,1)}) on (A={1,2,3}), why is (R) symmetric but not reflexive?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}) on (A={1,2,3}), which description fits (R) best?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}) on (A={1,2,3}), which pair will be in (R^{-1}) but not in (R)?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1)}) on (A={1,2,3}), which pairs must be added to make it an equivalence relation?Class 12Relations and FunctionsIntroduction to RelationsHard MathematicsIf the classes of (R) on (A={1,2,3,4}) are ({1,2}) and ({3,4}), which pair will not be in (R)?Class 12Relations and FunctionsIntroduction to RelationsHard